Bowyer signed off from his stint as caretaker boss alongside Terry McPhillips with a 1-1 draw at Wolves on Friday night, preserving his unbeaten record and ensuring he collected 10 points from a possible 12 since taking the reins from Henning Berg.
Appleton's switch from Blackpool to Lancashire rivals Rovers on a two-and-a-half-year deal was finally confirmed just two hours prior to kick-off, meaning he was not in attendance in the Black Country and instead watched the televised fixture.
Bowyer admitted he has enjoyed the role and asked what the future holds for himself, he replied: "We (he and McPhillips) knew what we were entering when we were asked to look after it. We've got a role at the club and we know what our role is, developing players.
"That is the role we will go back to, both myself and Terry with the Under-18s. We'll continue to do that."
Bowyer revealed Appleton called him before kick-off to send his best wishes, with Rovers' coaching staff, including new assistant Ashley Westwood, due to meet together on Monday.
Speaking about Appleton's appointment, Bowyer added: "We're delighted we've got a manager coming in who can provide us with some stability and he's worked under several good managers as well.
"He's a good coach, I know that from his youth days when he was in charge at West Brom. We're looking forward to working with him."
- Sports & Recreation